KTH Matematik  

Matematisk Statistik

Tid: 13 febuari 2012 kl 15.15-16.00.

Seminarierummet 3721, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!

Föredragshållare: Professor Professor Paavo Salminen, Matematiska institutionen, bo Akademi, bo, Finland

Titel: Optimal stopping of strong Markov processes

Abstract: The theory of optimal stopping is the crucial tool in, e.g.,

  • sequential statistical testing of hypotheses,
  • pricing of American options.
This survey talk is on methods for solving infinite horizon optimal stopping problems for continuous time strong Markov processes. Given a non-negative smooth reward function G the problem is to find a stopping time τ* such that

supτ∈M Ex(G(Xτ))= Ex(G(Xτ*))=

where X is the underlying process and M is the set of all stopping times in the natural filtration of X.

We focus on verification theorems obtained by

  • principle of smooth pasting,
  • Riesz representation for excessive functions,
  • representing excessive functions as expected suprema.
Some examples are presented, in particular, for Lvy processes. The talk is concluded with a short discussion on the historical development of the theory of optimal stopping.

Abstract as pdf-file.

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Sidansvarig: Filip Lindskog
Uppdaterad: 25/02-2009